## Chapter 4 Relations

¶In our everyday lives we encounter many circumstances which necessitate relating objects, sets, or people. Hiring is determined by comparing abilities of applicants and purchases are made based on relative prices. Descriptions such as “is faster than,” “is the brother of,” and “is smaller than” are heard countless times each day.

This concept of relating elements from different collections of objects is used extensively in mathematics. In previous courses, you have considered relations primarily from a very informal perspective; we will now approach the study of relations in a more formal way and give a formal definition of a relation below. A variety of special types of relations, including functions, will be considered in greater depth in this chapter.